Dynamics of popstar record sales on phonographic market -- stochastic model

Abstract

We investigate weekly record sales of the world's most popular 30 artists (2003-2013). Time series of sales have non-trivial kind of memory (anticorrelations, strong seasonality and constant autocorrelation decay within 120 weeks). Amount of artists record sales are usually the highest in the first week after premiere of their brand new records and then decrease to fluctuate around zero till next album release. We model such a behavior by discrete mean-reverting geometric jump diffusion (MRGJD) and Markov regime switching mechanism (MRS) between the base and the promotion regimes. We can built up the evidence through such a toy model that quantifies linear and nonlinear dynamical components (with stationary and nonstationary parameters set), and measure local divergence of the system with collective behavior phenomena. We find special kind of disagreement between model and data for Christmas time due to unusual shopping behavior. Analogies to earthquakes, product life-cycles, and energy markets will also be discussed.